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angle chasing in RMO, cyclic ABCD, 2 circumcircles, incenter, right wanted

Source: CRMO 2015 region 1 p1

September 30, 2018
geometrycircumcircleincenterright anglecyclic quadrilateral

Problem Statement

In a cyclic quadrilateral ABCDABCD, let the diagonals ACAC and BDBD intersect at XX. Let the circumcircles of triangles AXDAXD and BXCBXC intersect again at YY . If XX is the incentre of triangle ABYABY , show that ∠CAD=90o\angle CAD = 90^o.
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